It is known that one widely used technique for searching for oil or gas consists of seismic prospecting of subsurface formations. The geophysicist uses “seismic reflection” techniques to produce an image of subsurface formations. These techniques consist of emitting acoustic signals from the ground surface and recording them after successive reflections on interfaces between geological formations.
In land seismic exploration, seismic vibrations (compression and shear waves) are emitted from several points on the ground surface called shot points, and acoustic waves reflected by interfaces between geological formations called reflectors, are collected at different points on the surface using seismic receivers (geophones). Seismic receivers convert the reflected waves into electrical signals. There is a sufficient number of these receivers and they are laid out in such a manner that the recorded signals called traces form seismic data and can be used to image the structure of the geological layers.
In practice, the signal recorded by a seismic receiver has an amplitude that varies continuously as a function of time and the recorded peaks normally correspond to reflectors between layers. In reality, the interpretation of the data of a shot is much more complex. Firstly, waves can propagate through a first interface between layers and reflect on the next interface, and then on the first interface and so on before reaching the geophone. Secondly the amplitude of records reduces very quickly as a function of time. Therefore, records include peaks corresponding to multiple reflections or spurious reflections that should be eliminated before the structure of the subsurface can be correctly imaged.
A similar technique is used for seismic prospecting at sea, shots being carried out a few meters under the surface of the water and the seismic receivers or hydrophones themselves being located at the same depth. In this seismic prospecting method, the disadvantages mentioned above are amplified because the sea floor is highly reflecting, as well as air/water interfaces. Therefore one general purpose of this invention is to provide a method of seismic processing for at least partially eliminating undesirable signals corresponding to multiple reflections in records produced by receivers as a result of a seismic shot.
A number of seismic processing methods have been proposed in the past to attenuate multiple reflections in seismic records. These methods are based mainly on two techniques:                the first consists of using data to image the subsurface,        the second consists of modeling multiple reflections in order to subtract them from seismic data and thus to keep only useful seismic data, namely primary reflections, in order to image the subsurface.        
Verschuur et AI., 1992, [1], have presented a method in which seismic data are used to model multiple reflections in the two-dimensional domain. Van, Dedem and Verschuur, 1998, [2], also presented a generalization of the method to the three dimensional domain. In both cases, the method of modeling multiple reflections based on seismic data requires convolutions between acquired data traces and shot point traces located at receiver positions.
However, this method is disadvantageous in that there is no acquired shot point for each receiver location. Wiggins, 1988, [3] proposed another method using wave extrapolation techniques. In this method, Wiggins proposes to propagate data acquired on the surface through the water layer until the sea floor such that the former primary waves (incident waves) coincide in space with backward propagated multiple reflections (reflected multiple reflections). Adaptive subtraction operators between these two wavefields thus represent the reflectivity of the sea floor. However, this method has the disadvantage that it requires knowledge of the sea floor topography for adapting two propagated wave fields at the right position. Furthermore, the method was only presented in the two-dimensional domain.
In older work, Berryhill and Kim, 1986 [4] also proposed to use wave equation extrapolation for modeling peg-legs. Their method consists of making an wave equation extrapolation (redatuming) in the two-dimensional domain, in fact by using a Kirchhoff integral, of the recorded seismic data up to the selected sea floor, and then up to the surface. Once again, it suffices to know the wave propagation velocity in the water layer and the sea floor, in addition to the input shot points. Very recently, like Berryhill and Kim (1986), Lokshtanov, 2000, [5], showed an implementation for actual wave equation prediction, this time in the C-P domain. With this process, peg-legs in the water layer are subtracted using the sea floor layout. Reflection coefficients along the sea floor are supposed to be equal to 1 regardless of the propagation angle.
However, one disadvantage of the two methods mentioned above is the need for knowledge of the sea floor topography. In some cases (marine seismic exploration for very deep sea floor), this topography is unknown to geologists and it cannot be determined precisely enough to obtain usable results. One purpose of this invention is to provide a method for overcoming at least one of the above-mentioned disadvantages.